1. Field of the Invention
This invention generally relates to the scanned read-out of the photoresponses of photosensor arrays such as are employed in computed tomography systems and, more particularly, to the scanned read-out of the photoresponses in the digital rather than analog regime.
2. General Description of the Prior Art
CT scanners use a fan beam energy source, a central ray of which is projected through a particular point in space near the center of the object being scanned, as the energy source is stepped around a circular locus with center at that particular point in space. An arcuate strip of detector elements is located opposite the energy source on the other side of that particular point in space from the energy source and tracks the rotation of the energy source about that particular point in space. The object being scanned is always within the fan beam and absorbs a portion of the radiant energy in each contiguous segment of the fan beam, with the remnant radiant energy or "ray sum" in each segment of the fan beam being measured by a respective detector on the arcuate detector strip. The detector responses for each successive increment of rotation of the energy source and its opposing arcuate detector strip constitutes a separate "view" of the object being scanned. The detector responses during the successive views are digitized and stored in memory, since processing of these responses is not done in real time but rather is done after the scan is completed. During this subsequent processing the detector responses from each view are preweighted and prefiltered with a carefully formulated finite-impulse-response (FIR) filter kernel before being back projected into the image space to generate the gray scale values of the image picture elements or "pixels". The ray sums passing through each pixel center during each view are weighted and summed to create the gray scale value of the pixel by back projection. That is, since each ray sum represents the sum of the energy absorbed from a bundle of rays forming a segment of the fan beam in its traverse through successive portions of the object including the portion at which the pixel is located, the magnitude of the energy absorption ascribable to any one of the pixels traversed by that segment of the fan beam can be ascertained by performing an autocorrelation procedure involving all of the ray sums for bundles of rays passing through that pixel. This autocorrelation procedure suppresses the shadows cast by the pixels before and after the pixel of interest in the ray sums, which is the essence of producing a tomogram by computed tomography. In the additive combining of ray sums involved in implementing this autocorrelation procedure, each ray sum must be weighted to take into account the divergence of the fan beam before the ray packet associated with that pixel passes through that pixel.
Although the Fourier inversion approach to computed tomography has inherent speed advantage over back-projection reconstruction, it is considered to be unsuitable for use with the fan beam scanner because of excessive sensitivity to noise. The convolution and back-projection reconstruction method is suitable for view pipelining and yields images that are relatively free of undesirable artifacts from processing. A paper "Convolution reconstruction Techniques for Divergent Beams" by G.T. Herman, A.V. Lakshminarrayan and A. Naparstek appearing on pages 259-271 of COMPUTER BIOLOGIC MEDICINE, Vol 6, Oct. 1976, is of interest. So is a paper "Rapid Execution of Fan Beam Image Reconstruction Algorithms Using Efficient Computational Techniques and Special Purpose Processors" by B.K. Gilbert, S.K. Kenue, R.A. Robb, A. Chu, A.H. Lent and E.E. Swartzlander, Jr. appearing on pages 98-115 of the IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, Vol. BME-28, No. 2, Feb. 1981.
The strip of detector elements includes a linear array of several hundred or so scintillators and a linear array of several hundred or so photodiodes arrayed behind the linear array of scintillators. The scintillators convert the x-ray image into a light image, and the photodiodes convert the photons in elements of this light image to electric charge. The photodiodes are provided with respective preamplifiers providing a low input impedance for sensing photodiode current and providing a low output impedance for driving subsequent circuitry. Filtering is carried out to suppress the out-of-band portions of the wideband noise originating within the preamplifiers and the photodiodes that precede them. Doing this filtering before A/D conversion avoids the noise generating an alias in the A/D converter which noise alias falls within band. Customarily sample and hold circuitry is provided before each A/D converter to hold each successive view sample throughout the time period needed to complete the A/D conversion.
In more recent CT systems sold by General Electric Company the photodiode-preamplifier combinations are apportioned amongst subgroups of the entire group of such combinations, and the analog output voltages from the preamplifiers in each subgroup are time-division multiplexed to the input port of a shared analog-to-digital (or A/D) converter. In practice it has proven to be difficult to match the conversion characteristics of the A/D converters for the various subgroups owing to the need for a very high number of bits (i.e., 16-20 bits) of resolution in converter output signals in order to perform the back-projection calculations. The linearity of the conversion characteristics of the A/D converters is made as good as possible, but differences in the conversion characteristics cause "banding artifacts" in the final tomogram if the photodiodes in each subgroup of photodiode-preamplifier combinations are adjacent to each other in the strip of detector elements. These banding artifacts appear as intensity variations with considerable lower spatial frequency, so they are objectionably noticable to a human viewer of the final tomogram. To reduce the visibility of artifacts attributable to differences in the A/D converter conversion characteristics, the practice has been to scramble the locations in the strip of detector elements of the photodiodes in each subgroup of photodiode-preamplifier combinations, so there is lessened likelihood of low-spatial-frequency components of these artifacts in the tomogram, but increased likelihood of higher-spatial-frequency components of these artifacts in the tomogram. The higher-spatial-frequency components of these artifacts may also be low-pass spatially filtered again, if desired, with loss only of some high-spatial-frequency detail in the tomogram. The practice of scrambling the connections of photodiode-preamplifier combinations to the time-division-multiplexed A/D converters leads to undesirably complex electrical interconnections amongst the elements of the CT system, however, complicating data transfer using time-division multiplexing via a high-speed digital bus.
The practice of scrambling the connections of photodiode-preamplifier combinations to the time-division-multiplexed A/D converters interferes with the desire to locate the preamplifier and A/D converter as close to the photodiode as physically possible, in order to help minimize the pick-up of extraneous electrical signals as noise. The A/D converter and the preamplifiers time-division multiplexed to it are normally constructed in monolithic integrated circuit (IC) form, and extensive cabling is needed to connect the photodiodes to this IC where the photodiode scrambling practice is followed. Since the output impedance level of a photodiode is of the order of 30 megohms, the pick-up of extraneous electrical signals on the cabling is likely to be appreciable.
An alternative method of lessening the likelihood of low-spatial-frequency components of the artifacts of differences of A/D converter conversion characteristics is to provide each of the photodiode-preamplifier combinations with its own A/D converter. This design approach eliminates the self-correlation of A/D converter conversion characteristics that promotes the generation of banding artifacts, though artifacts of non-linearity can still occur on a clumped basis. General Electric Company constructed each of about seventy of the earliest CT scanners sold under the 7800 system number, using a respective dual-slope A/D converter for each of the 300 photodiodes in its scanner array. As higher scanner resolution was sought and as the number of photodiodes in the scanner array went up, however, this design approach appeared less attractive. It presented the problem of designing an A/D converter with sufficient linearity and number of bits of usable resolution to provide tomograms with acceptably low artifacts attributable to differences in the A/D converter conversion characteristics, but which is of compact and cheap enough construction to be used by the hundreds in each CT scanner.
It is known that high-resolution A/D signal conversion can be achieved with lower resolution components through the use of oversampled interpolative (or sigma-delta) modulation followed by digital low-pass filtering and then by decimation. Oversampling refers to operation of the modulator at a rate many times above the signal Nyquist rate, whereas decimation refers to subsampling so as to reduce the sample rate to the Nyquist rate. The ratio R of oversampling rate to the signal Nyquist rate is denominated "oversampling ratio". Sigma-delta A/D converters having single-bit quantizers in the overall feedback loops of their sigma-delta modulators can have very linear conversion characteristics as has been described by the inventor Ribner in his U.S. application Ser. No. 513,452 filed Apr. 23, 1990, entitled "PLURAL-ORDER SIGMA-DELTA ANALOG-TO-DIGITAL CONVERTERS USING BOTH SINGLE-BIT AND MULTIPLE-BIT QUANTIZATION" and assigned to General Electric Company. Accordingly, it is pointed out here, matching of the conversion characteristics of a plurality of sigma-delta A/D converters can be done quite easily, by designing them to have single-bit quantizers in the overall feedback loops of their sigma-delta modulators.
Detailed general information about sigma-delta A/D converters can be obtained from the following technical articles which are hereby incorporated by reference.
1) "A Use of Limit Cycle Oscillators to Obtain Robust Analog to Digital Converters", J.C. Candy, IEEE Transactions on Communications, Vol. COM-22, No. 3, pp. 298-305, Mar. 1974 PA0 2) "Using Triangularly Weighted Interpolation to Get 13-Bit PCM from a Sigma-Delta Modulator", J.C. Candy, et al., IEEE Transactions on Communications, Vol. COM-24, No. 11, pp. 1268-1275, Nov. 1976 PA0 3) "A Use of Double Integration in Sigma Delta Modulation", J.C. Candy, IEEE Transactions on Communications, Vol. COM-33, No. 3, pp. 249-258, Mar. 1985.
In the sigma-delta A/D converter, resolution is predominantly governed by two factors: (1) the oversampling ratio R, and (2) the "order" of the modulator. In a CT scanner it is advantageous to use a higher-order modulator since the oversampling ratio R need not be quite so large; given that there are hardware limitations on how short the duration of individual samples can be made, reducing the number of samples required for obtaining a specified bit resolution from the sigma-delta A/D conversion will reduce the time taken to acquire complete view data. "Order" in the present context is analogous to the order of a frequency selective filter and indicates the relative degree of spectral shaping that is provided by the sigma-delta modulator. As with a filter, higher selectivity is obtainable with a higher-order modulator at the expense of increased hardware complexity, particularly in the decimation filter required to suppress quantization noise from the modulator. Indeed, an FIR digital filter design that is suited for use in the decimation filter of a sigma-delta modulator to provide selectivity against quantization noise has a sinc.sup.(L+1) (.omega.T) response in the frequency domain where .omega. is radian frequency, T is the modulator period, and L is the order of the sigma-delta modulator. In line with commonplace terminology in the art of A/D converter design, sigma-delta modulators having an order of two or more are termed "higher-order" modulators in this specification and the appended claims.
In recognition of the resolution in the sigma-delta A/D converter being predominantly governed by oversampling ratio and by the "order" of the sigma-delta modulator, recent implementations of high-resolution oversampled analog-to-digital converters have employed both large oversampling ratios and higher-order sigma-delta modulators. However, practical considerations can limit the extent to which oversampling rate and modulator order can each be increased. For instance, for a given modulator clock rate (or oversampling rate), the oversampling ratio R is inversely proportional to the Nyquist rate after subsampling and thus cannot be made arbitrarily high without sacrificing conversion rate.
Different considerations set bounds on the modulator order. Implementations of order greater than two that use only a single quantizer can be shown to be only conditionally stable and are therefore not viable. Implementations of order greater than two that use more than one quantizer are described by the inventor in his U.S. application Ser. No. 513,452 filed Apr. 23 1990. Practical nonidealities--i.e., component mismatching, amplifier non-linearity, finite gain, excessive settling time, and limited signal dynamic range--normally limit resolution of prior-art higher-order sigma-delta analog-to-digital converter networks. U.S. Pat. application Ser. No. 550,763 filed Jul. 10, 1990, entitled "THIRD ORDER SIGMA DELTA OVERSAMPLED ANALOG-TO-DIGITAL CONVERTER NETWORK WITH LOW COMPONENT SENSITIVITY" and assigned to General Electric Company describes a third-order sigma-delta analog-to-digital converter network that exhibits significantly reduced sensitivity to these practical nonidealities.
The decimation filter included in the output circuitry of the sigma-delta A/D converter may simply be an accumulator operative as a simple integrator, or the decimation filter may be a sampled-data, low-pass, finite-impulse-response (FIR) filter followed by a subsampler. In either case, the decimation filter is a substantial, if not preponderant, portion of the entire sigma-delta converter as commonly constructed in metal-oxide-semiconductor integrated circuit form. The inclusion of the decimation filter makes the sigma-delta A/D converter compare unfavorably on a 1:1 basis with certain alternative integrated-circuit A/D converters from the standpoint of compactness. This is particularly so where the order of the sigma-delta A/D converter is higher and where the kernel of the FIR filter portion of the decimation filter includes a larger number of samples. The complexity of the decimation filter for a sigma-delta A/D converter is a factor that tends to lead one designing the electronics for a CT scanner to use a different type of A/D converter.
The inventor Ribner discerned that a sampled-data, low-pass, finite-impulse-response filter used in the decimation filter of the sigma-delta A/D converter can perform a dual function, by providing a substantial portion of the filtering needed to suppress high-frequency x-ray quantum noise and preamplifier noise before the detector responses are back projected into the image space to generate the gray scale values of the image picture elements or "pixels". Furthermore, the digital filtering otherwise needed to suppress high-frequency x-ray quantum noise and preamplifier noise generally has to have a sharp enough cut-off that it is comparable in complexity to the digital filtering required to suppress the quantization noise of a higher-order sigma-delta A/D converter. So, the digital low-pass filtering circuitry in the decimation filter can be eliminated from the comparison of the relative amounts of additional circuitry for a sigma-delta A/D converter and for alternative types of the sigma-delta A/D converter.
The inventor Ribner further discerned that sigma-delta A/D converters readily implement a CT scanner that can provide its operator increased bit resolution at the cost of increased image processing time. Such a CT scanner is implemented by changing the decimation filters to ones which have a different oversampling ratio.
Higher-order sigma-delta A/D converters of the type in which the decimation filter includes a sampled-data, low-pass, finite-impulse-response (FIR) filter followed by a subsampler have another problem that could lead one designing the electronics for a CT scanner to use a different type of A/D converter. Successive samples of the digital output signal from such a sigma-delta A/D converter tend to have considerable crosstalk between them because the kernel of the digital filter used to suppress higher-order quantization noise has to span more input samples (occurring at oversampling rate) than occur between successive output samples (occurring at a subsampled rate), as considered a pair at a time. This considerable crosstalk between successive output samples generated during successive views is a broadening of detector aperture that is unacceptable in CT scanner systems that use x-ray source wobbling. The back-projection reconstruction calculations cannot be carried out successfully in CT scanner systems that use x-ray source wobbling unless the successive view samples are more distinct from each other.
(Crosstalk between successive samples of the digital output signal from a sigma-delta A/D converter for sensor data is not as serious a problem in other image scanning systems, however. For example, in CT scanner systems that do not use x-ray source wobbling, the broadening of detector aperture caused by crosstalk between successive samples of the digital output signal from a sigma-delta A/D converter can be corrected for by spatial filtering, although the spatial filtering introduces additional noise into the system which can be avoided by minimizing crosstalk rather than using the spatial filtering. By way of example further afield, some image lag is tolerable in a television camera since there is some pixel-by-pixel integration in the eyes of the human viewer of a display generated from the camera output signal anyway.)
The inventors considered solving the crosstalk problem by increasing the oversampling rate by a factor L+1, presuming the order of the sigma-delta modulator is L and that the decimation filter of a sigma-delta modulator used to provide selectivity against quantization noise has a sinc.sup.(L+1) (.omega.T) frequency response, while maintaining the same oversampling ratio R. The periodicity of the sampling and holding of each successive view sample prior to A/D conversion is left unchanged. This causes the sigma-delta A/D converter to generate L digital output samples with crosstalk, which are discarded; then a subsequent output sample with no crosstalk, which is retained; L digital output samples with crosstalk, which are discarded; then a subsequent output sample with no crosstalk, which is retained etc. The problem with this procedure, which discards all output samples but every (L+1).sup.th ones, is that the concommitant increasing of the oversampling rate by the factor L+1 causes the equivalent noise bandwidth of the low-pass FIR digital filter in the decimation filter also to be increased by the factor L+1.
The inventors discerned that by increasing the oversampling rate by a factor (L+N), presuming the order of the sigma-delta modulator is L and that the decimation filter of a sigma-delta modulator used to provide selectivity against quantization noise has a sinc.sup.(L+1) (.omega.T) frequency response, the sigma-delta A/D converter would generate groups of N successive samples apparently free of intersample crosstalk interspersed by groups of L successive samples in which intersample crosstalk is apparent. By averaging the N successive samples apparently free of intersample crosstalk in each group and discarding the L successive samples in which intersample crosstalk is apparent, then subsampling by the factor (L+N), discarding the L successive samples in which intersample crosstalk is apparent does not increase the equivalent noise bandwidth as much.
The inventor Wu discerned that in practice a better overall CT scanner design could be one which accepts some crosstalk between successive digital output samples.
The inventor Ribner discerned how to avoid undesirable noise aliasing when an integrating preamplifier is used after each photodiode instead of a transresistive preamplifier. The ramp outputs from the integrating preamplifier are applied directly to the sigma-delta A/D converter thereafter, rather than being synchronously detected beforehand, and the low-pass digital filtering afforded by the decimation filter of the sigma-delta A/D converter extracts an averaged response to the samples of each ramp output taken at oversampling rate.